Furman led 14-3 at halftime on the strength of a 30-yard TD pass from Huff to Ryan Miller and a 10-yard touchdown run by Devin Abrams.
The Paladins wrapped it up with a 75-yard drive that took more than nine minutes off the clock in the fourth quarter, capped by Huff scoring on a 9-yard run. Grant Robinson later added a 25-yard touchdown run.
Huff completed 16 of 26 passes for 140 yards and Dominic Roberto had 98 yards rushing for Furman (10-2). Huff added 93 yards rushing and the Paladins had 251 yards on the ground.
The Phoenix (8-4) gained 315 yards but were 5-for-17 on third down, 1-for-5 on fourth and reached the red zone once.
Elon's Skyler Davis kicked 51- and 52-yard field goals, making him 7 of 8 on 50-plus-yard attempts this season. He tied the FCS single-season record for 50-plus-yard FGs. ULM's Jesse Garcia in 1983 and Western Carolina's Kirk Roach in 1987 were 7 of 12 each.
Furman was the Southern Conference runner-up and Elon finished tied for third in the Colonial Athletic Association.
Furman will play Incarnate Word in the second round.
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